Traditional analytical models in groundwater studies often simplify the complexities arising from spatial variations in aquifer geometry and anisotropy, limiting their ability to capture the full theoretical nuances of groundwater flow. In this study, we present a novel methodology that integrates geodesic distances within the intrinsic geometry of confined, constant-thickness aquifers, while also accounting for directional anisotropy in hydraulic properties. This approach provides a rigorous mathematical framework for accurately capturing the true distances along the aquifer geometry between pumping and observation wells, in contrast to traditional Euclidean distances. Our methodology is compatible with various analytical solutions, including the Theis (1935, https://doi.org/10.1111/jawr.1965.1.3.9) and Papadopulos and Cooper (1967, https://doi.org/10.1029/wr003i001p00241) solutions, extending their theoretical applicability to more complex aquifer geometries and anisotropic conditions. Numerical simulations of synthetic examples illustrate the theoretical consistency of the proposed approach, aligning drawdown patterns within this advanced framework. While primarily focused on enhancing existing analytical models, this methodology sets the stage for future theoretical advances in groundwater modeling, offering a conceptual expansion of analytical solutions to better address geometric and anisotropic complexities.

中文翻译：

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含水层水力建模分析框架中的测地线距离积分


地下水研究中的传统分析模型通常会简化含水层几何形状和各向异性空间变化所带来的复杂性，从而限制了它们捕捉地下水流的全部理论细微差别的能力。在这项研究中，我们提出了一种新的方法，该方法将测地线距离整合到承压、恒定厚度含水层的固有几何形状中，同时还考虑了水力特性中的定向各向异性。与传统的欧几里得距离相比，这种方法提供了一个严格的数学框架，用于准确捕获抽水和观察井之间沿含水层几何形状的真实距离。我们的方法与各种分析解决方案兼容，包括 Theis（1935 年，https://doi.org/10.1111/jawr.1965.1.3.9 年）和 Papadopulos 和 Cooper（1967 年，https://doi.org/10.1029/wr003i001p00241 年）解决方案，将它们的理论适用性扩展到更复杂的含水层几何形状和各向异性条件。合成示例的数值模拟说明了所提出的方法的理论一致性，在这个先进的框架内调整了回撤模式。虽然该方法主要侧重于增强现有的分析模型，但该方法为地下水建模的未来理论进步奠定了基础，提供了分析解决方案的概念扩展，以更好地解决几何和各向异性复杂性。